Direct numerical simulation of the weakly turbulent flow of non-Newtonian fluids is undertaken for two different generalised Newtonian theology models using a spectral element-Fourier method. Results for a power law (shear-thinning) rheology agree well with experimentally determined logarithmic layer correlations and with other previously published experimental work. As the flow index becomes smaller for the same Reynolds number, the flow deviates further from the Newtonian profile and the results suggest that transition is delayed. Predicted friction factors fall above those in the literature, but below the Newtonian values when a comparison is undertaken on the basis of the Metzner-Reed Reynolds number. Results for a Herschel-Bulkley model (yield stress + shear-thinning) are compared to corresponding experimental measurements and are found to be in very good agreement. Use of direct numerical simulation shows great promise in understanding transition and turbulence in non-Newtonian fluids. (C) 2004 Elsevier B.V. All rights reserved.